The initial value of Register A is 11011001, and we want to change it to 01101101. To achieve this, we perform a bitwise XOR operation with a mask. The mask that will flip the necessary bits is 10110100.
\[
\text{11011001} \, \text{XOR} \, \text{10110100} = 01101101
\]
Thus, performing XOR with the mask 10110100 changes the value of Register A to 01101101.
Therefore, the correct answer is 1. 10110100, XOR.